I had one of those once. It was not too bad, and with a blade in the right way round (teeth facing downwards, and facing towards you as you stand/sit in front of the machine) it should definitely cut. If NOT:
There is NO tension adjustment on that machine. The tension comes from inside the "arm" which is in fact 2 "halves"of press-fabricated sheet metal screwed together along the vertical axis. If you're quite sure that there is little or no blade tension then the answer is to remove the table, then unbolt the arm assembly from the machine, split it along the vertical line, then look inside. The big spring (maybe 2, I forget) up at the back of the arm near the On/off switch is either broken, badly stretched, or has come off either it's upper or lower retaining hook.
It is BTW a pretty crude machine by today's standards, but stripping it as above is not difficult, just very fiddly - you may learn a couple of new words! But fix (or replace) that spring/s if it's/they is/are broken/missing and it definitely WILL cut wood (and thin sheet metal with the fine blades).
BTW, if you look at that Youtube video linked in the post above, the bloke there says, quite correctly, that you can ONLY use Dremel's own scroll saw blades - not only are they pinned (not pinless) but they are MUCH shorter than any other scroll saw blade I've ever seen - as the bloke says, less than 3 inches (75 mm) long. If I remember correctly those Dremel blades come only in Coarse, Medium, and Fine cuts, no big ranges of TPIs like "proper" scroll saw blades. I MAYBE even have a couple of old Dremel blades kicking around somewhere.
But OTOH, though crude, somewhat clumsy, and lacking in just about all "modern" scroller's refinements it WILL cut wood (and thin metal). I used mine (mainly for cutting ply bits for model aeroplanes) and it lasted me years and years. In fact after scrapping the whole machine - the table is really horrible - I still have the rugged little motor saved from the machine in my "may come in handy one day" box.
HTH. Best of luck with it.